In 2012, the Texas standards (TEKS) were updated and the new fraction-related language is very similar to the wording in the CCSSM. When first introduced, it had teachers scratching their heads. There is a new emphasis on the unit fraction (1/b). Simply put, a unit fraction is a fraction with a numerator of 1–it is one part of a whole that has been divided into b equal parts. So 1/4, 1/6, and 1/20 are all unit fractions. Along with that, students are expected to understand the meaning of the numerator and the denominator.
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Today, I killed two birds with one stone using a classic Marilyn Burns Game, Cover-Up, from her book About Teaching Mathematics. I focused on the meaning of the denominator through the math talk we engaged in while playing.
We used plastic fraction tile kits to play, but you can have students create a fraction kit by folding paper strips. You also need a fraction cube with faces labeled to match your pieces. Ours was labeled 1/2, 1/3, 1/4, 1/6, 1/6, 1/12, and 1/12. Notice that there are more faces labeled with the smaller fractions. If you don’t have a fraction cube, you can create one using a cube with blank faces, or you can put stickers labeled with fractions on the faces of a standard number cube.
To summarize the game, players try to cover the whole with smaller unit fractions. They must cover it exactly–no overlap. We started by laying out the red whole piece (the piece labeled 1). Notice that I had my kiddos use dry erase markers to draw a number line under the fraction bar to connect with the idea that our whole is the space between 0 and 1 on the number line. That understanding has been an ongoing battle, and you can read more about it here. I rolled the fraction cube and got 1/3, so I placed the 1/3 piece on top of my whole. Here’s where I introduced the math talk. I modeled that for each turn, students were expected to (1) read the fraction and (2) explain the meaning of the denominator. For my roll of 1/3, it sounded like this: I have one-third. The denominator of 3 means that the whole is divided into 3 equal parts. That might seem easy enough, but it was actually enough of a struggle for the students that I wrote the second sentence on my whiteboard easel for them to refer to.
We all did that for our first round of turns. When it came back to me, I introduced the next level of math talk. This time around, and for the rest of the game, we would compare the fraction we just laid down with the fraction before it. I rolled 1/6 and laid it on the whole. I still had to read my fraction and explain the denominator: I have one-sixth. The denominator of 6 means the whole is divided into 6 equal parts. Next, I compared my fractions: 1/3 is greater than 1/6, because with three equal parts the parts are bigger than with six equal parts. More parts mean smaller pieces. Again, this was really a struggle for them, but we got lots of practice as the game progressed. For example, if I rolled 1/4 on my next turn, I would read my fraction, explain the denominator, and compare 1/6 and 1/4.
Combining a math game with math talk put the fun in practicing a fundamental concept!